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We present the &amp;mu; -calculus, a syntax for &amp;lambda;-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus <i>LK</i>, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and(More)
We review the relationship between abstract machines for (call-by-name or call-by-value) λ-calculi (extended with Felleisen's C) and sequent calculus , reintroducing on the way Curien-Herbelin's syntactic kit of the duality of computation. We provide a term language for a presentation of LK (with conjunction , disjunction, and negation), and we transcribe(More)
We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as the starting point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context. Our thesis is that the(More)
Categorical combinators [Curien 1986/1993; Hardin 1989; Yokouchi 1989] and more recently &#955;&sgr;-calculus [Abadi 1991; Hardin and Le&#180;vy 1989], have been introduced to provide an explicit treatment of substitutions in the &#955;-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special(More)